Energy of generalized distributions

We consider the energy of smooth generalized distributions and also of singular foliations on compact Riemannian manifolds for which the set of their singularities consists of a finite number of isolated points and of pairwise disjoint closed submanifolds. We derive a lower bound for the energy of all $q$-dimensional almost regular distributions, for each $q< \dim M,$ and find several examples of foliations which minimize the energy functional over certain sets of smooth generalized distributions.